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Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.
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Is this limit a tangent vector?
I am not sure this question is appropriate for this site but here is a proof.
By translation, we can suppose p=0. By rotation, we can suppose $\mathbb{R}^d=\mathbb{R}^{n+m}$ and $\mathbb{R}^n\times\{0 …